A perturbative analysis of geopotential disturbances for satellite cluster formation flying

Effects of the second order perturbative term of the Earth´s geopotential on clusters of satellites are analyzed by adding the linearized J₂ force onto the right side of Hill´s equations as a forcing function. A continuation of previous work, the equations of motion are generalized to orbits of all inclinations, and terms are identified that account for rotation of periapsis within the orbital plane, as well as precession of the longitude of the ascending node. The effect of the periapsis rotation on the cluster is identified as a `tumbling´ mode of the system. Accuracy of the linearization is determined by comparison of the analytic solutions with those obtained using an orbit propagator